The P-wave contributions have rather peculiar kinematic behaviours,
with cross sections becoming negative above certain threshold \(p_{\rm T}/M\)  values
and unphysical polarization parameters (\(|\lambda _\vartheta |>1\) ).
In fact, the calculations of the singlet and octet P-wave SDCs present singularities that match
(and can be cancelled by) the one appearing in the \({^3{\rm S}_1^{[8]}}\)  LDME [1]}, [2]}.
Therefore, only the \({^3{\rm P}_J^{[1,8]}} + {^3{\rm S}_1^{[8]}} \)  sum is required to be well-defined and physical,
while the two “fragments” \({^3{\rm P}_J^{[1,8]}}\)  and \({^3{\rm S}_1^{[8]}}\)  are, effectively,
an internal mathematical detail of the calculation, their relative contribution depending,
for example, on the choice of the unobservable NRQCD factorization scale.
In other words, the individual terms of the calculation are, on their own, unobservable.
In particular, the \({^3{\rm P}_J^{[1,8]}}\)  components at NLO contain large and negative transverse and/or longitudinal contributions,
leading to the kinematic peculiarities mentioned above.
While such characteristics can be acknowledged as technical details of a theoretical calculation
involving an expansion over purely mathematical objects, they are, nevertheless,
in striking contradiction with the universality of the \(p_{\rm T}/M\)  dependencies
of the cross sections and polarizations measured for the different quarkonium states.
The non-trivial \(p_{\rm T}/M\)  dependencies and sign-changing normalizations of the P-wave contributions
require seemingly miraculous cancellations to yield results that,
besides being physical, must reproduce the comparatively trivial experimental trends.
